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1 year ago

Dale, Thomas, and Betty plan to split the cost of a round-trip car ride from

Mathematics

2 answers:

beks73 [17]1 year ago

3 0

It would be 1649.04 cause 824.52+824.52=

Leno4ka [110]1 year ago

3 0

Answer: $\$549.68$

Step-by-step explanation:

Let be "b" the amount of money (in dollars) that Betty will have to pay for the round-trip.

According to the information provided in the exercise, the total cost of the trip from Oklahoma City to Sturgis was $824.52.

So, it the cost of the trip back will be the same, the total cost of the round-trip will be:

$Total\ cost=2(\$824.52)\\\\Total\ cost=\$1,649.04$

Since the exercise indicates that they plan to split that total cost for the round-trip in equal parts, you need to divide the Total cost of the round-trip by 3, in order to find "b".

Therefore, you get the following result:

$b=\frac{Total\ cost}{3}\\\\b=\frac{\$1,649.04}{3}\\\\b=\$549.68$

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If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

kiruha [24]

Answer:

$[1,\infty)$

Step-by-step explanation:

$b(x)=\sqrt{x-4}$

$a(x)=3x+1$

Since we want to know the domain of $(b \circ a)(x)$ , let's first consider the domain of the inside function, that is, that of $a(x)=3x+1$ . Every polynomial function has domain all real numbers.

So we can plug anything for function $a$ and get a number back.

Now the other function is going to be worrisome because it has a square root. You cannot take square root of negative numbers if you are only considering real numbers which that is the case with most texts.

Let's find $(b \circ a)(x)$ and simplify now.

$(b \circ a)(x)$

$b(a(x))$

$b(3x+1)$

$\sqrt{(3x+1)-4}$

$\sqrt{3x+1-4}$

$\sqrt{3x-3}$

Now again we can only square root positive or zero numbers so we want $3x-3 \ge 0$ .

Let's solve this to find the domain of $(b \circ a)(x)$ .

$3x-3 \ge 0$

Add 3 on both sides:

$3x \ge 3$

Divide both sides by 3:

$x \ge 1$

So we want $x$ to be a number greater than or equal to 1.

The option that says this is $[1,\infty)$

-------------------------------

Give an example why option A fails:

A number in the given set is -2.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(-2)=3(-2)+1=-6+1=-5$ and $b(-5)=\sqrt{-5-4}=\sqrt{-9} \text{ which is not real}$ .

Give an example why option B fails:

A number in the given set is 0.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(0)=3(0)+1=0+1=1$ and $b(1)=\sqrt{1-4}=\sqrt{-3} \text{ which is not real}$ .

Give an example why option D fails:

While all the numbers in set D work, there are more numbers outside that range of numbers that also work.

A number not in the given set that works is 3.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(3)=3(3)+1=9+1=10$ and $b(1)=\sqrt{10-4}=\sqrt{6} \text{ which is real}$ .

4 0

2 years ago

Read 2 more answers

Need help asap. Consider the diagram.

fgiga [73]

ANSWER

<em>alternate interior angles theorem</em>

EXPLANATION

According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.

From the above diagram line r is parallel to line s, therefore

$\angle \: 3 \cong \angle6$